Topic 4 understanding linear relationships

Front

What is a linear relationship?

Back

A linear relationship is a relationship between two variables that can be represented by a straight line on a graph. It can be expressed in the form of an equation, typically y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope of a line represent?

Back

The slope of a line represents the rate of change between the two variables. It indicates how much y changes for a unit change in x.

Front

What is the y-intercept in a linear equation?

Back

The y-intercept is the value of y when x is 0. It represents the starting point of the relationship on the y-axis.

Front

How do you determine if a relationship is proportional?

Back

A relationship is proportional if the ratio of y to x is constant for all pairs of coordinates (x, y). This means that the line passes through the origin (0,0).

Front

What does a positive slope indicate?

Back

A positive slope indicates that as x increases, y also increases. This shows a direct relationship between the two variables.

Front

What does a negative slope indicate?

Back

A negative slope indicates that as x increases, y decreases. This shows an inverse relationship between the two variables.

Front

How can you find the slope from two points?

Back

The slope (m) can be calculated using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points.

Front

What is the formula for the slope-intercept form of a linear equation?

Back

The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope represent in a real-world context?

Back

In a real-world context, the slope can represent a rate of change, such as speed, cost per item, or growth rate.

Front

What is the significance of the y-intercept in a real-world scenario?

Back

The y-intercept often represents a starting value or initial condition in a real-world scenario, such as a fixed cost before any variable costs are added.